INDIANAPOLIS -- Backup quarterback Josh McCown wants to remain in Chicago, but a market that seems to be heating up for his services could change that.

Tampa Bay Buccaneers general manager Jason Licht wants to add a veteran quarterback to compete with Mike Glennon, as does new Bucs coach Lovie Smith. Given Smith’s familiarity with McCown from their time together in Chicago, the veteran quarterback is a logical option to battle Glennon for the starting job.

“There’s a lot of positions on our team that I’m sure Lovie would agree that we want to anoint as the starter,” Licht said when asked if Glennon is the starting quarterback. “We want competition for Mike.”

McCown produced a 3-2 record last season filling in for Jay Cutler, generating a passer rating of 109 and throwing 13 touchdown passes and only one interception. McCown has expressed a desire on multiple occasions to remain with the Chicago Bears, as he was an integral part of the team's implementing a new offense under first-year Bears coach Marc Trestman.

But the Bears are expected to face competition for McCown, who at this point appears to be inclined to remain in Chicago unless he’s given an opportunity to start or handed significantly better financial terms in a contract than his current team can offer.

“I talk to Josh pretty much weekly, or biweekly. I’ve talked to him two or three times, anyway, and I’ve texted with him,” Trestman said Thursday at Lucas Oil Stadium. “He’s in the loop into what’s going on. I’ve just called him on a personal level just to catch up with him and see how he sees the league and what’s going on. We just like to talk football. He knows exactly where he stands with us. I think that he’s going to take his time, see where things are at. When he’s ready to say, ‘I want to come back,’ I know [general manager] Phil [Emery] is going to do everything he can, and we’re going to do everything can to make sure he is.”

The Bears haven’t yet submitted an offer to McCown, and because he signed a one-year contract in 2013 under the minimum-salary benefit, the team can’t officially sign him until the start of free agency (March 11), although the sides could agree to a deal anytime before that date. So McCown could be exposed to the market (if the sides don’t agree to a new deal before the league new year), where he’s sure to have plenty of suitors.

“I’d like to see him come back,” Cutler said at the end of last season. “There’s talks about him getting other opportunities, which I think, rightfully so, he’ll have. We’ve had candid talks about what he wants to do. I’ll let Josh address that when he wants to. I know we’d love to have him back. We’d like to have him back in the building. Just the amount of work he does behind the scenes with the younger players and myself, just the experience he brings to the quarterback room, it’s very valuable. We’ll see how it works out. The guys in the locker room are hoping to see Number 12 back next year.”